问题 填空题
lim
n→∞
[n(1-
1
3
)(1-
1
4
)(1-
1
5
)…(1-
1
n+2
)]
等于______.
答案

lim
n→∞
[n(1-
1
3
)(1-
1
4
)(1-
1
5
)…(1-
1
n+2
)]

=

lim
n→∞
(n×
2
3
×
3
4
×…×
n+1
n+2
)

=

lim
n→∞
2n
n+2

=2.

故答案为:2.

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